The assumptions have a quite different character. Inequalities (REF ) are ranges for the physical parameters; we expect the
existence of travelling waves in this parameter regime. The uniform
upper bound of (REF ) is expected to hold, but it should be
derived from the system of equations, which we did not succeed to do.
The regularity estimate (REF ) and the local
regularity (REF ) can be shown with the tools of
elliptic regularity theory, see [1]}. We
formulate them here as assumptions, since the regularity theory is not
the focus of this contribution.
